1 Triggers and settings

2 Import Data

Note: for Neah Bay in 2016

  1. There are not algae data for the South Area only, the North.
  2. There are are only two transects of invert data for the North. There are 5 transects in the South area.

3 By KELP SPECIES but summed across all urchins

## `summarise()` has grouped output by 'site', 'year', 'zone', 'area', 'transect'.
## You can override using the `.groups` argument.
## `summarise()` has grouped output by 'site', 'year'. You can override using the
## `.groups` argument.

3.1 Individual plot version

The following splits the facet into individual plots for better plotting and labeling.

## `summarise()` has grouped output by 'site', 'year', 'zone', 'area', 'transect'.
## You can override using the `.groups` argument.
## `summarise()` has grouped output by 'site', 'year'. You can override using the
## `.groups` argument.

## `summarise()` has grouped output by 'site', 'year', 'zone', 'area', 'transect'.
## You can override using the `.groups` argument.
## `summarise()` has grouped output by 'site', 'year'. You can override using the
## `.groups` argument.

## `summarise()` has grouped output by 'site', 'year', 'zone', 'area', 'transect'.
## You can override using the `.groups` argument.
## `summarise()` has grouped output by 'site', 'year'. You can override using the
## `.groups` argument.
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

## `summarise()` has grouped output by 'site', 'year', 'zone', 'area', 'transect'.
## You can override using the `.groups` argument.
## `summarise()` has grouped output by 'site', 'year'. You can override using the
## `.groups` argument.

## `summarise()` has grouped output by 'site', 'year', 'zone', 'area', 'transect'.
## You can override using the `.groups` argument.
## `summarise()` has grouped output by 'site', 'year'. You can override using the
## `.groups` argument.
## `geom_smooth()` using formula = 'y ~ x'

## `summarise()` has grouped output by 'site', 'year', 'zone', 'area', 'transect'.
## You can override using the `.groups` argument.
## `summarise()` has grouped output by 'site', 'year'. You can override using the
## `.groups` argument.

3.2 Site x Year regressions for urchins vs kelp

## 
## Call:
## lm(formula = Kelp ~ Urchins, data = nereo[nereo$site == "Tatoosh Island", 
##     ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.2240 -0.4312 -0.2485  0.5608  1.4392 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)   1.2614     0.6582   1.916    0.104
## Urchins       0.2176     0.4320   0.504    0.632
## 
## Residual standard error: 0.9187 on 6 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.04058,    Adjusted R-squared:  -0.1193 
## F-statistic: 0.2538 on 1 and 6 DF,  p-value: 0.6324
## 
## Call:
## lm(formula = Kelp ~ Urchins, data = nereo[nereo$site == "Destruction Island", 
##     ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.7381 -0.6178  0.1280  0.4375  0.7938 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)   0.8137     0.2701   3.013   0.0236 *
## Urchins      -0.2925     0.9198  -0.318   0.7612  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6494 on 6 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.01658,    Adjusted R-squared:  -0.1473 
## F-statistic: 0.1011 on 1 and 6 DF,  p-value: 0.7612
## 
## Call:
## lm(formula = Kelp ~ Urchins, data = ptery[ptery$site == "Tatoosh Island", 
##     ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.6070 -0.3621 -0.1145  0.2932  0.9539 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)   0.4419     0.3984   1.109   0.3098  
## Urchins       0.8263     0.2615   3.161   0.0196 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.556 on 6 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.6247, Adjusted R-squared:  0.5622 
## F-statistic: 9.989 on 1 and 6 DF,  p-value: 0.01955
## 
## Call:
## lm(formula = Kelp ~ Urchins, data = ptery[ptery$site == "Destruction Island", 
##     ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.29180 -0.09352  0.02426  0.11111  0.20435 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.51085    0.07857   6.502  0.00063 ***
## Urchins     -0.15486    0.26756  -0.579  0.58379    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1889 on 6 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.05288,    Adjusted R-squared:  -0.105 
## F-statistic: 0.335 on 1 and 6 DF,  p-value: 0.5838

4 Total for each.

I know we’re not supposed to combine macro & nereo but…just to see

## `summarise()` has grouped output by 'site', 'year', 'zone', 'area'. You can
## override using the `.groups` argument.
## `summarise()` has grouped output by 'site'. You can override using the
## `.groups` argument.

5 BY SPECIES

5.1 Transect level, all depths

## 
## Attaching package: 'cowplot'
## The following object is masked from 'package:ggpubr':
## 
##     get_legend
## The following object is masked from 'package:lubridate':
## 
##     stamp
## Loading required package: viridisLite

## By Site and Depth level

## `summarise()` has grouped output by 'year', 'site', 'zone'. You can override
## using the `.groups` argument.
## `summarise()` has grouped output by 'year', 'site', 'zone'. You can override
## using the `.groups` argument.
## [1] 1020    7
## [1] 340   5
## [1] 255   5

correlation purple vs nereo at Tatoosh r = 0.2147361, p = 0.0484337

5.2 By Site and 5 m only

## `summarise()` has grouped output by 'year', 'site', 'zone'. You can override
## using the `.groups` argument.
## `summarise()` has grouped output by 'year', 'site', 'zone'. You can override
## using the `.groups` argument.
## [1] 1020    7
## [1] 340   5
## [1] 255   5
## $x
## [1] "Urchin density"
## 
## $y
## [1] "Kelp density"
## 
## $colour
## [1] "Site"
## 
## attr(,"class")
## [1] "labels"

5.3 By site, averaged across depths, data = years

## `summarise()` has grouped output by 'year', 'site'. You can override using the
## `.groups` argument.
## `summarise()` has grouped output by 'year', 'site'. You can override using the
## `.groups` argument.
## [1] 540   7
## [1] 180   4
## [1] 135   4

## [1] NA
## [1] NA

This plot compared to the previous is interesting.

  1. At the transect level, there is a negative correlation between urchin density and kelp neroycystis density at Tatoosh

  2. At the site level, there is a positive correlation for Nerocystis (r = NA) and for Pterogophora (r = NA)at Tatoosh across years.

6 TATOOSH

6.1 By transect

## 
## Formula: Y ~ a * exp(k * X)
## 
## Parameters:
##   Estimate Std. Error t value Pr(>|t|)    
## a   1.9829     0.3557   5.575 2.93e-07 ***
## k  -0.1109     0.0717  -1.547    0.126    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.935 on 84 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.406e-06
##          a          k 
##  1.9829546 -0.1109077
## [1] 361.5355

7 Across years

## `summarise()` has grouped output by 'year', 'site', 'area', 'zone'. You can
## override using the `.groups` argument.
## `summarise()` has grouped output by 'year'. You can override using the
## `.groups` argument.

8 Coastwide urchin - kelp patterns

8.1 All kelp: Nereo + Macro + Ptero

## `summarise()` has grouped output by 'year', 'site', 'area', 'zone'. You can
## override using the `.groups` argument.
## `summarise()` has grouped output by 'year'. You can override using the
## `.groups` argument.

cor: r = 0.7456971; p = 0.0210725

8.2 Canopy only

## `summarise()` has grouped output by 'year', 'site', 'area', 'zone'. You can
## override using the `.groups` argument.
## `summarise()` has grouped output by 'year'. You can override using the
## `.groups` argument.

cor r = 0.534885

8.3 Nero only

## `summarise()` has grouped output by 'year', 'site', 'area', 'zone'. You can
## override using the `.groups` argument.
## `summarise()` has grouped output by 'year'. You can override using the
## `.groups` argument.

8.4 Macro only

## `summarise()` has grouped output by 'year', 'site', 'area', 'zone'. You can
## override using the `.groups` argument.
## `summarise()` has grouped output by 'year'. You can override using the
## `.groups` argument.

## Ptero only

## `summarise()` has grouped output by 'year', 'site', 'area', 'zone'. You can
## override using the `.groups` argument.
## `summarise()` has grouped output by 'year'. You can override using the
## `.groups` argument.

cor r = 0.7032538; = 0.034552

9 Tatoosh only

## `summarise()` has grouped output by 'site', 'year', 'transect', 'area'. You can
## override using the `.groups` argument.
## 
## Formula: Y ~ a * exp(k * X)
## 
## Parameters:
##   Estimate Std. Error t value Pr(>|t|)    
## a  1.33515    0.16320   8.181 2.63e-12 ***
## k -0.13208    0.08223  -1.606    0.112    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9816 on 84 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 5.016e-06
##          a          k 
##  1.3351476 -0.1320835
## [1] 244.8431

## `summarise()` has grouped output by 'site', 'year', 'transect', 'area'. You can
## override using the `.groups` argument.

## `summarise()` has grouped output by 'site', 'year', 'transect', 'area'. You can
## override using the `.groups` argument.
## 
## Formula: Y ~ a * exp(k * X)
## 
## Parameters:
##   Estimate Std. Error t value Pr(>|t|)    
## a  1.60569    0.26098   6.153 2.49e-08 ***
## k -0.01246    0.07727  -0.161    0.872    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.776 on 84 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 3.804e-06
##           a           k 
##  1.60569036 -0.01245511
## [1] 346.7817

## `summarise()` has grouped output by 'site', 'year', 'transect', 'area'. You can
## override using the `.groups` argument.
## 
## Formula: Y ~ a * exp(k * X)
## 
## Parameters:
##   Estimate Std. Error t value Pr(>|t|)    
## a   1.9070     0.3590   5.312 8.73e-07 ***
## k  -0.2230     0.1577  -1.414    0.161    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.984 on 84 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 4.821e-06
##          a          k 
##  1.9070384 -0.2230188
## [1] 365.9036

10 Combined Figure 5

## `summarise()` has grouped output by 'year', 'site', 'area', 'zone'. You can
## override using the `.groups` argument.
## `summarise()` has grouped output by 'year'. You can override using the
## `.groups` argument.
## `geom_smooth()` using formula = 'y ~ x'

## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
## 
## Attaching package: 'gridExtra'
## 
## 
## The following object is masked from 'package:dplyr':
## 
##     combine
## 
## 
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

11 Kelp vs Kelp

## `summarise()` has grouped output by 'site', 'year'. You can override using the
## `.groups` argument.

Correlations between kelps

Macro vs Nereocystis, all sites r = -0.3779968 with p = 0.0104645

Macro vs Nereocystis, two sites r = 0.0648126 with p = 0.798334

Macro vs Pterygophora, all sites r = 0.1636673 with p = 0.2826962

Macro vs Nereocystis, all sites r = 0.1209657 with p = 0.4286285

12 Correlations at Tatoosh Island across years (yearly means) for different depth zones

A different, and simplified version of the above for just tatoosh and faceted by species.

Essentially, there are different relationships at different depths. Probably too much detail for this manuscript.

## `summarise()` has grouped output by 'year', 'site', 'area', 'zone', 'transect'.
## You can override using the `.groups` argument.
## `summarise()` has grouped output by 'site', 'year', 'zone'. You can override
## using the `.groups` argument.